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Homework Help: Two representation

  1. Jan 8, 2014 #1
    1. The problem statement, all variables and given/known data
    ##e = \begin{bmatrix}
    1 & 0 \\[0.3em]
    0 & 1 \\[0.3em]

    \end{bmatrix}##,
    ##a =\frac{1}{2} \begin{bmatrix}
    1 & -\sqrt{3} \\[0.3em]
    -\sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##.
    ##b =\frac{1}{2} \begin{bmatrix}
    1 & \sqrt{3} \\[0.3em]
    \sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##
    ##c= \begin{bmatrix}
    -1 & 0 \\[0.3em]
    0 & 1 \\[0.3em]

    \end{bmatrix}##
    ##d=\frac{1}{2} \begin{bmatrix}
    -1 & \sqrt{3} \\[0.3em]
    -\sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##
    ##f=\frac{1}{2} \begin{bmatrix}
    -1 & -\sqrt{3} \\[0.3em]
    \sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##
    This is irreducible representation of group ##S_3##. \\
    Reducible representation of ##S_3## is
    ##e=d=f = \begin{bmatrix}
    1 & 0 \\[0.3em]
    0 & 1 \\[0.3em]

    \end{bmatrix}##
    ##a =b=c=\frac{1}{2} \begin{bmatrix}
    -1 & -\sqrt{3} \\[0.3em]
    -\sqrt{3} & 1 \\[0.3em]

    \end{bmatrix}##
    Why is better to use irreducible then reducible representation in this case and in general?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 8, 2014 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What do you mean by "better to use?" You haven't used any representations to do anything.
     
  4. Jan 9, 2014 #3
    In practice one always take some irreducible representation to work with. My question is why?
     
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